Given $ m \angle ABC = 7x - 5$, and $ m \angle CBD = 7x + 115$, find $m\angle CBD$. $B$ $A$ $D$ $C$
Explanation: From the diagram, we see that together ${\angle ABC}$ and ${\angle CBD}$ form ${\angle ABD}$ , so $ {m\angle ABC} + {m\angle CBD} = {m\angle ABD}$ Since $\angle ABD$ is a straight angle, we know ${m\angle ABD = 180}$ Substitute in the expressions that were given for each measure: $ {7x - 5} + {7x + 115} = {180}$ Combine like terms: $ 14x + 110 = 180$ Subtract $110$ from both sides: $ 14x = 70$ Divide both sides by $14$ to find $x$ $ x = 5$ Substitute $5$ for $x$ in the expression that was given for $m\angle CBD$ $ m\angle CBD = 7({5}) + 115$ Simplify: $ {m\angle CBD = 35 + 115}$ So ${m\angle CBD = 150}$.